Concept explainers
The expression for the change in length of the line segment.
Answer to Problem 52P
The expression for the change in length of the line segment is
Explanation of Solution
Given information:
The flow is symmetric about x axis.
Write the expression for the two-dimensional velocity field in the
Here, the horizontal speed is
Write the expression for the velocity component along x direction.
Here, the variable is
Write the expression for the velocity component along x direction.
Here, the variable is
Write the expression for the velocity in x direction in differential form.
Write the expression for the initial length.
Here, the initial location of A is
Write the expression for the final length.
Here, the final location of A is
Write the expression for the change in lengths.
Calculation:
Substitute
Integrate the Equation (VIII).
Substitute
Substitute
Substitute
Substitute
Conclusion:
The expression for the change in length of the line segment is
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Chapter 4 Solutions
Fluid Mechanics: Fundamentals and Applications
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